Electric Potential Energy & Electric Potential Honors Physics Mr. Kuffer

Electric Potential Energy & Electric Potential

Honors Physics Mr. Kuffer

We Know… Coulomb’s Law

If either Q1 or Q2 increases the Force increases

If either Q1 or Q2 decreases the Force decreases

If r, the distance between the two charges, increases the force decreases

If r, the distance between the two charges, decreases the force increases

Because r appears as 1/r2 the dependence on r is strong

Q1 r Q2

We know… Coulomb’s Law

Double r. F decreases by a factor of 4

If r -> r/3 F increases by a factor of 9

If r decreases to ¼ of its value,

F becomes 16 times as large

Q1 r Q2

We know… The Electric Field

The electric field is the force on a small charge, divided by the charge:

Fields play an intermediate role in the force between bodies.We treat fields as a property of space. Charges create fields. Given the field we can calculate the forces on ANY charged objects

Field Lines

The electric field between two closely spaced, oppositely charged parallel plates is constant.

Today’s Topics

• Electric Potential Energy• Electric Potential• Electric Equi-potential Lines

Recall… Work

• You do work when you push an object up a hill• The longer the hill the more work you do: more

distance• The taller the hill, the more work you do: more force

The work, W, done on an object by an agent exerting a constant force is the product of the component of the force in the direction of the displacement and the magnitude of the displacement

dFW ||

Energy is capacity to do worknote Ep aka UG

• Gravitational Potential Energy• Kinetic Energy• Energy can be converted into other forms of

energy • When we do work on any object we transfer

energy to it • Energy cannot be created or destroyed

mghUG

2

2

1mvK

GU

GUKW

Potential Energy

The presence of charges can give rise to a potential energy (PE)

Ug doing work!! Ue doing work!!

Potential EnergyWe determined the

potential energy Uel of a spring by asking how much work we do to compress it.

We can determine the potential energy of a charge distribution by how much work we do to bring the charge to its position

Potential of a Parallel-Plate Capacitor

Slide 21-24

Potential Energy• High Gravitational PE. Ball will roll down hill

• High Electrical Potential Energy• Positive charge will move away

• Positive charge will “fall” from high • potential energy to low PE +

• Negative charge “falls” from high PE to• low PE -

•

Electric Potential Energycharges also have electrical potential energy

EEF 0q

+Q

+Q

d

FdW

Edq0

EdqU e 0

vNote the loss in potential Energy.Hence the ‘-’ sign

Electric Potential Energy

• Work done (by electric field) on charged particle is qEd

• Particle has gained Kinetic Energy (qEd)• Particle must therefore have lost

Potential Energy U=-qEd

Electrostatic Potential Energy

Change in electric potential energy is work done against electric force (from b to a):

PEa – PEb = qEd

a---

Compare Ug b---

Ug = mg (a-b) =mgh

Electric Potential

• Just as Electric field depends on space and allows us to compute force on any charge, Electric Potential depends on space and allows us to calculate Uelec for any charge.

(Not Electric Potential Energy)

Electric Potential

0q

UV

compare with the Electric Field and Coulomb Force

0q

FE

If we know the potential field this allows us to calculate changes in potential energy for any charge introduced

VqU 0 EF 0q

Electrostatic Potential Energy and Potential Difference

Electric potential is defined as potential energy per unit charge:

Unit of electric potential: the volt (V).

1 V = I J/C.

qVU elec

q

UV elec

Greater at B, Greater yet at C

Ue= qV

Ue= q V Ue(B) = 10 nC * 400V


Analogy between gravitational and electrical potential energy:

A

B

Which has higher potential energy A, B or C the same?

A and B are the same distance from sphere

A

B

Which has higher potential energy A, B or C the same?


A

B

Which is at a higher potential (voltage)A,B or C the same?


A

B

Which is at a higher potential (voltage)A,B or C the same?

(electric potential is a "property" related only to the electric field itself)


Careful here!Potential is a measure per individual charge!


Only changes in potential can be measured, allowing free assignment of V = 0… where there is no change there is no potential difference.

Vba = Vb – Va = Ue(b) –Ue (a)

q

Therefore Potential (V) is unaffected by position change within equipotential surfaces!

For Potential Difference… defining ‘zero’ is arbitrary… just like choosing a frame of reference for Ug

Electric Potential

Electric Potential is a scalar

it is defined everywhere

but it does not have any direction

it doesn’t depend on a charge being there

Super Fun Review Challenge!

Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f?

+ i f

Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f?

+ i f

Is the change in Ue ΔU, A) positive B) negativeC) zeroas a negative charge moves from point labeled i to f?

+ i f

Is the change in Ue ΔU, A) positive B) negativeC) zeroas a negative charge moves from point labeled i to f?

+ i f

Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f? + -

i f

Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f? + -

i f

Conceptual Example Problem

Slide 21-17

The correct order of electrical potentials from largest to smallest is A)V1>V2>V3B)V1=V2> V3C)V1=V2 =V3D)V3>V2=V1E)V3>V2>V1

Note: q1, q2, & q3 are positive test charges


Slide 21-17

The correct order of electrical potentials from largest to smallest is A)V1>V2>V3B)V1=V2> V3 C)V1=V2 =V3D)V3>V2=V1E)V3>V2>V1

Note:1 and 2 share an equipotential surface.


Slide 21-17


Note: q1, q2, & q3 are positive test charges


Slide 21-17


Note: We are asked about the Electric Potential… not the Force the charge Feels!

Energy Conservation in Electric Potentials

• Just as for mechanical systems Energy is conserved. We can change potential energy to kinetic energy and vice versa.

• Kf + qVf = Ki + qVi

• Kf –Ki = qVi –q Vf =-q(Vf –Vi)

ΔK = -qΔV

The more Potential is lost… the more Kinetic is gained

Charged Particle Moving Through a Potential Difference

Slide 21-18ΔK = -qΔV

Charged Particle Moving Through a Potential Difference

Slide 21-18

Be careful! Things are reversed for negative charge.Negative charge speeds up if it moves from region of lower to higher potential: ΔK = -qΔV

The Electron Volt, a Unit of Energy

One electron volt (eV) is the energy (not charge) gained by an electron moving through a potential difference of one volt.

Slide 21-19

Example ProblemA proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point?

Slide 21-20

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Electric Potential Energy & Electric Potential Honors Physics Mr. Kuffer